Download Multinomial Logit Regression Analysis on 1991 General Social Survey Data and more Study notes Sociology in PDF only on Docsity! Sociology multinomial logit testing hypotheses The data for this exercise again comes from the 1991 General Social Survey. The categorical dependent variable occ is coded as follows: occ=0 if a workers occupation is laborer, operative or craft; occ=1 if occupation is clerical, sales, or service; occ=2 if occupation is managerial, technical, or professional. The independent variables are: educ is years of schooling; age is age in years; sexx is coded 1 male, 0 female; rural is coded 1 if grew up in rural area, 0 otherwise; mid and wst are dummy variables for region, with other parts of the country omitted. Let’s fit what we’ll treat for most of this exercise as the null model. 3. mlogit occ educ age sexx rural mid wst,base(0) Multinomial regression Number of obs = 633 LR chi2(12) = 353.13 Prob > chi2 = 0.0000 Log likelihood = -511.92941 Pseudo R2 = 0.2564 ------------------------------------------------------------------------------ occ | Coef. Std. Err. z P>|z| [95% Conf. Interval] ---------+-------------------------------------------------------------------- 1 | educ | .2490034 .056606 4.399 0.000 .1380577 .3599492 age | .0156041 .0099216 1.573 0.116 -.0038418 .0350501 sexx | -2.028054 .2392113 -8.478 0.000 -2.4969 -1.559209 rural | -.7635868 .2619814 -2.915 0.004 -1.277061 -.2501126 mid | .4081406 .2761675 1.478 0.139 -.1331378 .9494189 wst | .4151271 .3078639 1.348 0.178 -.188275 1.018529 _cons | -2.253103 .853224 -2.641 0.008 -3.925391 -.5808147 ---------+-------------------------------------------------------------------- 2 | educ | .7840261 .0684775 11.449 0.000 .6498126 .9182395 age | .01764 .011552 1.527 0.127 -.0050015 .0402816 sexx | -1.680553 .2778157 -6.049 0.000 -2.225062 -1.136044 rural | -.128399 .2965349 -0.433 0.665 -.7095968 .4527988 mid | .144635 .3137103 0.461 0.645 -.4702258 .7594958 wst | .3873871 .3445527 1.124 0.261 -.2879237 1.062698 _cons | -10.27188 1.063177 -9.661 0.000 -12.35567 -8.188092 ------------------------------------------------------------------------------ Tests of individual coefficients You can use the z-scores to test for individual coefficients in separate equations. To do a test of ALL the coefficients of a given variable, say educ, in all the equations, you need to impose the constraint of the null hypothesis, and then estimate the restricted model: docsity.com 4. mlogit occ age sexx rural mid wst,base(0) Multinomial regression Number of obs = 633 LR chi2(10) = 112.28 Prob > chi2 = 0.0000 Log likelihood = -632.35198 Pseudo R2 = 0.0815 ------------------------------------------------------------------------------ occ | Coef. Std. Err. z P>|z| [95% Conf. Interval] ---------+-------------------------------------------------------------------- 1 | age | .0139588 .0095435 1.463 0.144 -.0047461 .0326637 sexx | -1.941273 .2293351 -8.465 0.000 -2.390762 -1.491785 rural | -.9540048 .2512577 -3.797 0.000 -1.446461 -.4615487 mid | .5754085 .2641193 2.179 0.029 .0577443 1.093073 wst | .476824 .2938117 1.623 0.105 -.0990362 1.052684 _cons | .8674283 .418339 2.074 0.038 .0474989 1.687358 ---------+-------------------------------------------------------------------- 2 | age | .0103217 .0094321 1.094 0.274 -.0081648 .0288082 sexx | -1.213865 .2267656 -5.353 0.000 -1.658317 -.7694121 rural | -.7604203 .2414063 -3.150 0.002 -1.233568 -.2872726 mid | .4151938 .2612787 1.589 0.112 -.096903 .9272906 wst | .4373206 .2893423 1.511 0.131 -.1297799 1.004421 _cons | .6000712 .4171453 1.439 0.150 -.2175186 1.417661 ------------------------------------------------------------------------------ (Outcome occ==0 is the comparison group) The likelihood ratio test statistic is then This is distributed as a chi-square with 2 degrees of freedom. Since the mean of a chisquare with df=2 is 2, 242 is way into any reasonable critical region. Another way to do this same test (i.e., that all the educ coefficients are zero) is with a Wald statistic produced by Stata’s test command. After fitting the full alternative model with command 3 above, issue the following command: 5. test educ ( 1) [1]educ = 0.0 ( 2) [2]educ = 0.0 chi2( 2) = 146.29 Prob > chi2 = 0.0000 docsity.com
